
from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors

def a__       (			A_   ):






  '''simple docstring'''





  __magic_name__								=			prime_factors(A_   )
  if is_square_free(A_   ):
    return -1 if len(A_   ) % 2 else 1
  return 0


if __name__ == "__main__":
    import doctest

    doctest.testmod()



from __future__ import annotations

def a__       (			A_,	A_   ):






  '''simple docstring'''





  if b == 0:
    return (1, 0)
  ((__magic_name__)	,       (__magic_name__))								=			extended_euclid(A_,	a % b   )
  __magic_name__								=			a // b
  return (y, x - k * y)

def a__       (			A_,	A_,	A_,	A_   ):






  '''simple docstring'''





  ((__magic_name__)	,       (__magic_name__))								=			extended_euclid(A_,	A_   )
  __magic_name__								=			na * na
  __magic_name__								=			ra * x * na + ra * y * na
  return (n % m + m) % m

def a__       (			A_,	A_   ):






  '''simple docstring'''





  ((__magic_name__)	,       (__magic_name__))								=			extended_euclid(A_,	A_   )
  if b < 0:
    __magic_name__								=			(b % n + n) % n
  return b

def a__       (			A_,	A_,	A_,	A_   ):






  '''simple docstring'''





  __magic_name__	,       __magic_name__								=			invert_modulo(A_,	A_   ), invert_modulo(A_,	A_   )
  __magic_name__								=			na * na
  __magic_name__								=			ra * x * na + ra * y * na
  return (n % m + m) % m


if __name__ == "__main__":
    from doctest import testmod

    testmod(name='chinese_remainder_theorem', verbose=True)
    testmod(name='chinese_remainder_theorem2', verbose=True)
    testmod(name='invert_modulo', verbose=True)
    testmod(name='extended_euclid', verbose=True)

